Course Policies Math 302 Advanced Cryptography, Spring 2025

Overview

This course is a follow-up to Math 202 Cryptography. During the first part of the semester, we will revisit a few of the topics from Math 202 to fill in some of the more mathematically sophisticated details, such as attacks on the Discrete Log Problem, primality testing, and elliptic curve cryptography.

We will spend the majority of the second half of the semester looking at encryption schemes that are considered to be safe from attacks by quantum computers, including lattice-based systems and learning-with-errors schemes. We also work to understand CRYSTALS-Kyber and CRYSTALS-Dilithium, which are module-learning-with-errors systems recently chosen in summer 2024 by NIST as the standard for post-quantum encryption.

We're going to be learning a lot of new ideas together. This is going to be a really fun semester!

Goals for a 300-level Mathematics Course

By the end of this semester you should:

• Be able to formulate a concise, precise mathematical arguments and proofs, including recognizing when it is complete or when further justification is needed
• Be able to read and communicate advanced technical concepts
• Be willing to approach a problem even if you do not know whether or not your approach will be successful. If it doesn't work out, try something else!
• Appreciate the necessity of rigorous mathematical arguments
• Continue in your development from being a consumer of mathematics to being a producer of mathematics

Goals Specific to Cryptography

You should gain a deeper understanding of:

• The distinction between a theoretic solution and a practical solution
• How to generate parameters, including large prime numbers, used for RSA, DHKE, and DSA
• Attacks to solve the Discrete Log problem, including the Pohlig-Hellman algorithm and Pollard's \( \rho\) method
• The underlying group structure of elliptic curves and how this is used in elliptic curve cryptography
• The basic theory underlying lattice-based systems
• The basic theory of module-learning-with-errors systems and the implementation in CRYSTALS-Kyber and CRYSTALS-Dilithium

Expectations

One of the features that makes your Wheaton education so special is that we have time in small classes to explore material together. The class meetings are not intended to be a complete encapsulation of the course material, but instead will focus on the major concepts from the readings and videos to clarify the more subtle ideas in the course.

You should expect to put in approximately 3 hours outside of class for each scheduled hour of class. In other words, expect to spend a roughly 9 hours per week on Cryptography outside of the scheduled class meetings. There will be some weeks where you spend more time, and there may be some weeks where you spend slightly less.

The Honor Code

We operate under the Wheaton Honor Code for all of your academic work at Wheaton. This carries certain freedoms and responsibilities for both you as a student and me as a professor. I take this quite seriously.

Most likely, no Honor Code issues will arise this semester. If you are uncertain about whether a particular situation falls under the Honor Code, then please consult with me. However, if an Honor Code issue does come up, I will assume that you are prepared for the full consequences. Remember that you should write out, and sign, the following statement on all course work:

"I have abided by the Wheaton College Honor Code in this work."

Evaluation

Your final grade will be determined by

Pre-Class Assignments	5%
Class Engagement/Participation	15%
Problem Sets, Kryptos Contest,	50%
& Presentation
Two Take-home Exams	30%

Pre-Class Assignments

The purpose of reading the text and watching the optional videos before class is that if you are familiar with the basic concepts and definitions, then the class meetings can be devoted to the major ideas and subtleties of the material. Mathematical understanding is built in stages, and you will absorb the material more quickly if the class meetings are your second exposure to the fundamental ideas.

The Pre-Class Assignments are posted on the course webpage and include three or so questions that you should be able to answer after you have completed the reading and viewed any videos. You will submit your responses through Canvas.

I will grade the Pre-Class Assignments using a binary scale: If you make a serious attempt, you will get full credit, even if your answers are not completely correct. The purpose of these questions is to encourage you to engage with the material before class. If you've read the text and watched any videos but don't understand how to answer a question, it is perfectly fine to say "I did the prep work but don't see how to approach this question."" You'll definitely understand by the end of the end of the week!

Notice that the Pre-Class Assignments are due at 9:00 am on Monday! This will give me enough time to review your responses before our class on Monday. You will be allowed to drop one Pre-Class assignment at the end of the semester.

Class Engagement/Participation

A significant part of the class meetings will be devoted to working in small groups on problems that delve more deeply into the content introduced in the Pre-Class Assignments and discussed at the beginning of class. A substantial amount of your learning will happen during these collaborative sessions by bouncing ideas off of other students and seeing how other groups approach the problems. I will also determine your Engagement/Participation grade for each class meeting using a binary scale: You were present and engaged with your peers or you weren't.

However, I also know that there may be times when you have a valid reason for missing class. I'll be really flexible, so if you need to miss class, please let me know. Let's just keep the lines of communication open.

Problem Sets and Kryptos

You will have a Problem Set due most weeks of the semester. You will be allowed to drop one Problem Set assignment at the end of the semester.

I firmly believe that one of the best ways to build your understanding of mathematics is to explore the ideas with other students. Therefore, I strongly encourage you to discuss the Problem Sets with other students outside of class. However, the answers that you give should represent your own thinking about solutions, and you must each write up your own solutions independently.

Under no circumstances can you look at another student's write-up or share your write-up with another student! If you do work with other students, you must cite them on your on a Problem Set solutions. If you fail to do this, I will view it as a violation of the Honor Code.

You will also participate in Krytpos 2025, a national undergraduate cryptanalysis contest organized by Central Washington University and held April 10 - 14. For this contest, you will work in groups of two or three of your own choosing. The idea of the contest is that you will be given a ciphertext, and your goal is to recover the original English plaintext.

You will have several supplemental problems to help you practice for Kryptos. An important point to note about these problems: I do not expect that you will break every cipher! It's great if you do, but you can receive full credit on these assignments even if you do not find the original plaintext. You will turn in a one to two page writeup that explains your analysis that allowed you to find the plaintext or the different approaches you attempted if you were unable to break the cipher. In the latter case, you will be evaluated on the quality of your failure.

There will be a Final Problem Set due during Finals Week that will consist of a few problems based on content not covered on the exams as well as a cumulative component. This assignment will count for the equivalent of two Problem Sets. You cannot drop this assignment.

Group Presentation

There are many interesting applications of cryptography outside of the syllabus that we should all know more about, and you'll get to explain one of these to the rest of the class! You will form groups of two of your own choosing, and your group will give a 30 minute presentation during last week of class. I will give more details about the Group Presentation during the semester.

Take-home Exams

The purpose of the exams is for you to demonstrate your understanding of the course material and, just as importantly, to give you feedback on where your understanding is strong and where you may need more work. Similar to last fall, the exams will be open-note take-home exams where you will have several days to work on them. See the Tentative Daily Syllabus for dates of the exams. I will provide more details about the structure of the exams as the time gets closer.

I know that exams can be stressful, especially with the other academic, extracurricular, and family commitments that you may have. To try to reduce some of this stress concerning your grade, I will weight your exam scores by differing amounts: The lower of your exam scores will count for 1/3 of your exam grade, and the higher score will count for 2/3 of your exam grade.

Getting Help with Cryptography

Please come see me during my drop-in office hours! No appointment necessary! If you have a conflict and cannot make my office hours, please email me and we can set up an appointment for another time.

Remember that the goal of the course is to help you learn Cryptography and develop your mathematical thinking! If there's any point where you feel that the structure of the class isn't working for you, please come by and we can figure out some possible strategies.

Other Resources and Support

The college maintains a fuller list of Resources and Support for Spring 2025.